A fundamental problem in the study of networks is that of understanding their large-scale structure. Methods drawn from statistics and machine learning, especially maximum likelihood methods, can help. In this talk I’ll describe, with accompanying examples, a suite of methods developed in recent years that can shed light on things like community structure, hierarchy, and status (or ranking) within networks. I’ll also describe some intriguing connections between these methods and other areas of physics and engineering, including spin-glass theory, signal processing, and the fundamental limits of computation.